Problem: A circle has a sector with area $\dfrac{57}{2}\pi$ and central angle $\dfrac{19}{12}\pi$ radian. What is the area of the circle? ${36\pi}$ $\color{#9D38BD}{\dfrac{19}{12}\pi}$ ${\dfrac{57}{2}\pi}$
Answer: The ratio between the sector's central angle $\theta$ and $2 \pi$ radians is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{2 \pi} = \dfrac{A_s}{A_c}$ $\dfrac{19}{12}\pi \div 2 \pi = \dfrac{57}{2}\pi \div A_c$ $\dfrac{19}{24} = \dfrac{57}{2}\pi \div A_c$ $A_c \times \dfrac{19}{24} = \dfrac{57}{2}\pi$ $A_c = \dfrac{57}{2}\pi \times \dfrac{24}{19}$ $A_c = 36\pi$